International Journal of Modern Physics C

The numerical approach to a large class of one- and two-dimensional Fokker–Planck equations (FPE) often encountered in modeling Brownian Motors is presented. The method is based on Finite Element scheme with additional modifications for specific problems. We compare results from discretization of FPE with those obtained from Monte Carlo (MC) simulation of the corresponding Langevin equations. Accuracy, efficiency and applicability are also discussed.

A brief introduction to the simulation of stochastic differential equations is presented. Algorithms to simulate rare fluctuations, a topic of interest in the light of recent theoretical work on optimal paths are studied. Problems connected to the treatment of the boundaries and correlated noise will also be discussed.

A previously introduced model (B. Cleuren and C. Van den Broeck, Europhys. Lett.54, 1 (2001)) is studied numerically. Pure negative mobility is found for the minimum number of three interacting walkers.

Collective instabilities in globally coupled pendulums driven by parametric modulation is numerically investigated. Parametric instabilities are suppressed by mutual synchronization despite individual pendulums are under a parametric resonance condition. On the other hand, continuous collective rotation can be parametrically excited with certain modulation frequencies outside the regular parametric resonance.

The problem of escape of a Brownian particle in a cusp-shaped metastable potential is of special importance in nonadiabatic and weakly-adiabatic rate theory for electron transfer (ET) reactions. For the weakly-adiabatic reactions, the reaction follows an adiabaticity criterion in the presence of a sharp barrier. In contrast to the nonadiabatic case, the ET kinetics can be, however considerably influenced by the medium dynamics. In this paper, the problem of the escape time over a dichotomously fluctuating cusp barrier is discussed with its relevance to the high temperature ET reactions in condensed media.

An AC driven, noiseless, underdamped Brownian particle moving on an asymmetric periodic substrate provides an interesting example of deterministic ratchet: In the adiabatic regime periodic and chaotic trajectories coexist on fine tuning the amplitude of the input signal; the transition from regular to chaotic transport happens through an intermediate class of trajectories exhibiting confined chaos.

We consider two types of Go models of a protein (crambin) and study their kinetics through molecular dynamics simulations. In the first model, the residue–residue contact interactions are selected based on a cutoff distance, R_c. The folding times strongly depend on the value of R_c and nonmonotonically. This indicates a need for a physically determined set of native contacts. One may accomplish it by considering the van der Waals radii of the residual atoms and checking if the atoms overlap. In the second model, non-native attractive contacts are added to the system. This leads to bad foldability. However, for a small number of such extra contacts there is a slight acceleration in the kinetics of folding.

Analytical and numerical results on the ordering role of external random fluctuations in excitable systems are presented. Our study focuses on a simple model for excitable systems. Regular waves are created and sustained out of noise when the system is forced with random perturbations. Explicit results for the generation and dynamics of rings and targets are presented.

In this paper we consider a chemical process, for which the reagent of interest decays shortly after it is created. For such a system the standard theory of nonequilibrium spatial correlations in the density fluctuations, which leads to Ornstein–Zernike type of expression, does not work. We compare results of molecular simulations with another theoretical description based on the assumption that the lifetime of the reagent is short enough to treat its motion as a ballistic rather than diffusive one.

Numerical simulations of a dissipative hard sphere gas reveal a dependence of the cooling rate on correlation of the particle velocities due to inelastic collisions. We propose a coefficient which characterizes the velocity correlations in the two-particle velocity distribution function and express the temperature decay rate in terms of this coefficient. The analytical results are compared with numerics.

Nonequilibrium molecular dynamics (NEMD) simulations of fluids are generally based on either a DOLLS or SLLOD tensor algorithm. The former is always considered to be a Hamiltonian system, but not particularly useful in high strain rate flow simulations, while the latter is not considered to be a Hamiltonian system, but much more practical and accurate in flow simulations. We demonstrate herein using noncanonical transformations of the particle momenta of the system that the SLLOD equations, when written in terms of appropriate noncanonical variables, are completely Hamiltonian, whereas the DOLLS equations are not so. A modified set of DOLLS equations in terms of the noncanonical variables which again is completely Hamiltonian is also derived. Both algorithms then lead to a phase space distribution function which is canonical in both the coordinates and momenta.

According to a phenomenological phase transition mechanism introduced quite recently, we propose a systematic examination of the polymorphic contraction–expansion effects observed for a broad class of morphologies with nonvanishing surface (line) tension. In our mean-field approach, we are looking for the line order parameter behavior as a function of a thermodynamic control parameter at a fixed number of entities consituting the morphology as a whole. We also wish to somehow invert the problem, and will be looking for some evolution going via a set of quasi-equilibrium states while fixing the control parameter. Both the situations considered are of interest for studying the so-called morphology diagrams as well as, to some extent, for describing selected model evolutions in a two-dimensional microworld, e.g., in nanoscale, where biomembranes and interfaces are presently of special attention.

A unidimensional diffusion in a potential field of induced stress is considered. The way from random walk (RW) to limiting partial differential equation (Smoluchowski equation) for standard and time dependent RW is shown. A technologically important case of gold dispersion in crystallizing polymer swollen by acetone vapor is analyzed. Theoretical predictions based on Smoluchowski equation with time dependent coefficients are found to be in very good agreement with experimental data.